World energy supplies are often measured in the unit of quadrillion British thermal units (10^12 btu), generally called a "quad." In 2015, world energy consumption is projected to be 5.81*10^17kJ.
Current annual energy consumption in the United States is 99.3 quads. Assume that all this energy is to be generated by burning CH4(g) in the form of natural gas. If the combustion of the CH4(g) were complete and 100% efficient, how many moles of CH4(g) would need to be combusted in order to provide the U.S. energy demand?
I am clueless as to how to solve this. My teacher did not go over this material so if someone could show me step by step how to solve this, that would be very much appreciated!!
You want to check my work very carefully. The long way of doing this is to write and balance th equation, and use stoichiometry to calculate grams CH4 need then convert that to mols. I've tried a shorter route and if you use it you may learn how to shorten some calculations also.
First I went to google and let google convert 99.3 quads BTU to megajoules. That's about 1.05E12 MJ. Then I found a page on the internet that gave the combustion of CH4 to be 38 megajoules/cubic meter. Google converts 1 cubic meter to 1000 L and 1000 L/22.4 L/mol = about 44/6 mols so 38 MJ/m^3 = 38 MJ/44.6 mol.
38 MJ/44.6 mol x # mols = 1.05E12 MJ.
And solve for # mols.
If you haven't used google for conversions yet, try it. For example covert 22.4 L to cubic meters. Type in the google window "22.4 L to cubic meters" without the quotation marks and hit the enter button. You will get the answer that 22.4L = 0.0224 cubic meters.
To solve this problem, we need to use the given information, the molecular formula of CH4 (methane), and some conversion factors.
Step 1: Convert the given energy consumption from quads to joules.
1 quad = 1 × 10^15 btu
1 btu = 1055.06 joules
So, 5.81 × 10^17 kJ = 5.81 × 10^17 × 10^3 joules (since 1 kJ = 10^3 joules) = 5.81 × 10^20 joules.
Step 2: Determine the energy released by burning one mole of methane (CH4).
The balanced chemical equation for the combustion of methane is as follows:
CH4(g) + 2O2(g) → CO2(g) + 2H2O(g)
From the balanced equation, we know that for each mole of CH4 reacted, one mole of CO2 and two moles of H2O are produced.
The enthalpy change (∆H) for burning one mole of methane (CH4) is approximately -890 kJ/mol.
Step 3: Use the energy conversion to find the number of moles of CH4.
Let's assume the combustion of methane is 100% efficient, meaning all of the energy released is used.
From step 1, we know that the U.S. energy demand is 5.81 × 10^20 joules.
Using the energy conversion, we can set up the following equation:
5.81 × 10^20 joules = (X moles CH4) × (-890 kJ/mol)
Solve this equation for X by rearranging the equation:
(X moles CH4) = (5.81 × 10^20 joules) / (-890 kJ/mol)
Now, convert kJ to joules by multiplying by 1000:
(X moles CH4) = (5.81 × 10^20 joules) / (-890 kJ/mol) × (1000 joules/kJ)
Simplifying this equation gives:
(X moles CH4) = (5.81 × 10^20) / (-890 × 1000) mol
Step 4: Calculate the result.
Now, perform the calculation to find the number of moles of CH4 that would be needed to provide the U.S. energy demand.
(X moles CH4) ≈ 6.52 × 10^14 mol
Therefore, approximately 6.52 × 10^14 moles of CH4 would need to be combusted to provide the U.S. energy demand.
Note: The negative sign in the calculation indicates that the energy is being released during the combustion process.